If I have a figure with 4 damage and 2 targets, can I make a ranged attack against both another figure and a barrier? (If successful, I would deal 1 damage to the other figure, and 3 to break the barrier; if unsuccessful, all the damage would go towards breaking the barrier.)

Thanks in advance.

Nope. From the DR rule book, page 34:

Destroying blocking terrain. A square of blocking terrain can be destroyed by an attack that deals at least 3 damage in a single attack. When a character attacks blocking terrain, the attack automatically succeeds. An attacker may not target both a character and blocking terrain with the same attack. A close combat attack may be used to target and destroy a square of blocking terrain adjacent to the square the character occupies. A ranged combat attack may be used to destroy a square of blocking terrain by drawing a line of fire to the center of the square of blocking terrain; the line of fire is not blocked by blocking terrain in the target square.

However, if you have 2 targets and 6 Dmg (from perplex, of course), you can target 2 barriers/objects... just not figures and terrain per NV's reason